<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>1</b></div></td><td><div><a href="index.php?section=problems&amp;id=1" style="text-decoration:none;" title="Click to view problem">
Add all the natural numbers below one thousand that are multiples of 3 or 5.
</a></div></td><td><div style="text-align:center;">106465</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>2</b></div></td><td><div><a href="index.php?section=problems&amp;id=2" style="text-decoration:none;" title="Click to view problem">
Find the sum of all the even-valued terms in the Fibonacci sequence which do not exceed four million.
</a></div></td><td><div style="text-align:center;">88801</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>3</b></div></td><td><div><a href="index.php?section=problems&amp;id=3" style="text-decoration:none;" title="Click to view problem">
Find the largest prime factor of a composite number.
</a></div></td><td><div style="text-align:center;">65050</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>4</b></div></td><td><div><a href="index.php?section=problems&amp;id=4" style="text-decoration:none;" title="Click to view problem">
Find the largest palindrome made from the product of two 3-digit numbers.
</a></div></td><td><div style="text-align:center;">60567</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>5</b></div></td><td><div><a href="index.php?section=problems&amp;id=5" style="text-decoration:none;" title="Click to view problem">
What is the smallest number divisible by each of the numbers 1 to 20?
</a></div></td><td><div style="text-align:center;">68921</div></td></tr>

<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>6</b></div></td><td><div><a href="index.php?section=problems&amp;id=6" style="text-decoration:none;" title="Click to view problem">
What is the difference between the sum of the squares and the square of the sums?
</a></div></td><td><div style="text-align:center;">70408</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>7</b></div></td><td><div><a href="index.php?section=problems&amp;id=7" style="text-decoration:none;" title="Click to view problem">
Find the 10001<sup>st</sup> prime.
</a></div></td><td><div style="text-align:center;">58829</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>8</b></div></td><td><div><a href="index.php?section=problems&amp;id=8" style="text-decoration:none;" title="Click to view problem">
Discover the largest product of five consecutive digits in the 1000-digit number.
</a></div></td><td><div style="text-align:center;">52559</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>9</b></div></td><td><div><a href="index.php?section=problems&amp;id=9" style="text-decoration:none;" title="Click to view problem">
Find the only Pythagorean triplet, {<var>a</var>, <var>b</var>, <var>c</var>}, for which <var>a</var> + <var>b</var> + <var>c</var> = 1000.
</a></div></td><td><div style="text-align:center;">52412</div></td></tr>

<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>10</b></div></td><td><div><a href="index.php?section=problems&amp;id=10" style="text-decoration:none;" title="Click to view problem">
Calculate the sum of all the primes below two million.
</a></div></td><td><div style="text-align:center;">47451</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>11</b></div></td><td><div><a href="index.php?section=problems&amp;id=11" style="text-decoration:none;" title="Click to view problem">
What is the greatest product of four numbers on the same straight line in the 20 by 20 grid?
</a></div></td><td><div style="text-align:center;">36434</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>12</b></div></td><td><div><a href="index.php?section=problems&amp;id=12" style="text-decoration:none;" title="Click to view problem">
What is the value of the first triangle number to have over five hundred divisors?
</a></div></td><td><div style="text-align:center;">31598</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>13</b></div></td><td><div><a href="index.php?section=problems&amp;id=13" style="text-decoration:none;" title="Click to view problem">
Find the first ten digits of the sum of one-hundred 50-digit numbers.
</a></div></td><td><div style="text-align:center;">36742</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>14</b></div></td><td><div><a href="index.php?section=problems&amp;id=14" style="text-decoration:none;" title="Click to view problem">
Find the longest sequence using a starting number under one million.
</a></div></td><td><div style="text-align:center;">35121</div></td></tr>

<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>15</b></div></td><td><div><a href="index.php?section=problems&amp;id=15" style="text-decoration:none;" title="Click to view problem">
Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner?
</a></div></td><td><div style="text-align:center;">28733</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>16</b></div></td><td><div><a href="index.php?section=problems&amp;id=16" style="text-decoration:none;" title="Click to view problem">
What is the sum of the digits of the number 2<sup>1000</sup>?
</a></div></td><td><div style="text-align:center;">38735</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>17</b></div></td><td><div><a href="index.php?section=problems&amp;id=17" style="text-decoration:none;" title="Click to view problem">
How many letters would be needed to write all the numbers in words from 1 to 1000?
</a></div></td><td><div style="text-align:center;">24210</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>18</b></div></td><td><div><a href="index.php?section=problems&amp;id=18" style="text-decoration:none;" title="Click to view problem">
Find the maximum sum travelling from the top of the triangle to the base.
</a></div></td><td><div style="text-align:center;">24684</div></td></tr>

<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>19</b></div></td><td><div><a href="index.php?section=problems&amp;id=19" style="text-decoration:none;" title="Click to view problem">
How many Sundays fell on the first of the month during the twentieth century?
</a></div></td><td><div style="text-align:center;">22703</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>20</b></div></td><td><div><a href="index.php?section=problems&amp;id=20" style="text-decoration:none;" title="Click to view problem">
Find the sum of digits in 100!
</a></div></td><td><div style="text-align:center;">37266</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>21</b></div></td><td><div><a href="index.php?section=problems&amp;id=21" style="text-decoration:none;" title="Click to view problem">
Evaluate the sum of all amicable pairs under 10000.
</a></div></td><td><div style="text-align:center;">24496</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>22</b></div></td><td><div><a href="index.php?section=problems&amp;id=22" style="text-decoration:none;" title="Click to view problem">
What is the total of all the name scores in the file of first names?
</a></div></td><td><div style="text-align:center;">23151</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>23</b></div></td><td><div><a href="index.php?section=problems&amp;id=23" style="text-decoration:none;" title="Click to view problem">
Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
</a></div></td><td><div style="text-align:center;">16282</div></td></tr>

<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>24</b></div></td><td><div><a href="index.php?section=problems&amp;id=24" style="text-decoration:none;" title="Click to view problem">
What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
</a></div></td><td><div style="text-align:center;">20105</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>25</b></div></td><td><div><a href="index.php?section=problems&amp;id=25" style="text-decoration:none;" title="Click to view problem">
What is the first term in the Fibonacci sequence to contain 1000 digits?
</a></div></td><td><div style="text-align:center;">28494</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>26</b></div></td><td><div><a href="index.php?section=problems&amp;id=26" style="text-decoration:none;" title="Click to view problem">
Find the value of <i>d</i> &lt; 1000 for which 1/<i>d</i> contains the longest recurring cycle.
</a></div></td><td><div style="text-align:center;">13996</div></td></tr>

<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>27</b></div></td><td><div><a href="index.php?section=problems&amp;id=27" style="text-decoration:none;" title="Click to view problem">
Find a quadratic formula that produces the maximum number of primes for consecutive values of <i>n</i>.
</a></div></td><td><div style="text-align:center;">14695</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>28</b></div></td><td><div><a href="index.php?section=problems&amp;id=28" style="text-decoration:none;" title="Click to view problem">
What is the sum of both diagonals in a 1001 by 1001 spiral?
</a></div></td><td><div style="text-align:center;">21980</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>29</b></div></td><td><div><a href="index.php?section=problems&amp;id=29" style="text-decoration:none;" title="Click to view problem">
How many distinct terms are in the sequence generated by <i>a<sup>b</sup></i> for 2 &le; <i>a</i> &le; 100 and 2 &le; <i>b</i> &le; 100?
</a></div></td><td><div style="text-align:center;">18398</div></td></tr>

<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>30</b></div></td><td><div><a href="index.php?section=problems&amp;id=30" style="text-decoration:none;" title="Click to view problem">
Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
</a></div></td><td><div style="text-align:center;">20238</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>31</b></div></td><td><div><a href="index.php?section=problems&amp;id=31" style="text-decoration:none;" title="Click to view problem">
Investigating combinations of English currency denominations.
</a></div></td><td><div style="text-align:center;">13779</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>32</b></div></td><td><div><a href="index.php?section=problems&amp;id=32" style="text-decoration:none;" title="Click to view problem">
Find the sum of all numbers that can be written as pandigital products.
</a></div></td><td><div style="text-align:center;">11813</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>33</b></div></td><td><div><a href="index.php?section=problems&amp;id=33" style="text-decoration:none;" title="Click to view problem">
Discover all the fractions with an unorthodox cancelling method.
</a></div></td><td><div style="text-align:center;">13013</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>34</b></div></td><td><div><a href="index.php?section=problems&amp;id=34" style="text-decoration:none;" title="Click to view problem">
Find the sum of all numbers which are equal to the sum of the factorial of their digits.
</a></div></td><td><div style="text-align:center;">17790</div></td></tr>

<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>35</b></div></td><td><div><a href="index.php?section=problems&amp;id=35" style="text-decoration:none;" title="Click to view problem">
How many circular primes are there below one million?
</a></div></td><td><div style="text-align:center;">16111</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>36</b></div></td><td><div><a href="index.php?section=problems&amp;id=36" style="text-decoration:none;" title="Click to view problem">
Find the sum of all numbers less than one million, which are palindromic in base 10 and base 2.
</a></div></td><td><div style="text-align:center;">17980</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>37</b></div></td><td><div><a href="index.php?section=problems&amp;id=37" style="text-decoration:none;" title="Click to view problem">
Find the sum of all eleven primes that are both truncatable from left to right and right to left.
</a></div></td><td><div style="text-align:center;">13280</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>38</b></div></td><td><div><a href="index.php?section=problems&amp;id=38" style="text-decoration:none;" title="Click to view problem">
What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, ... ?
</a></div></td><td><div style="text-align:center;">10978</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>39</b></div></td><td><div><a href="index.php?section=problems&amp;id=39" style="text-decoration:none;" title="Click to view problem">
If <i>p</i> is the perimeter of a right angle triangle, {<i>a</i>, <i>b</i>, <i>c</i>}, which value, for <i>p</i> &le; 1000, has the most solutions?
</a></div></td><td><div style="text-align:center;">13166</div></td></tr>

<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>40</b></div></td><td><div><a href="index.php?section=problems&amp;id=40" style="text-decoration:none;" title="Click to view problem">
Finding the <i>n</i><sup>th</sup> digit of the fractional part of the irrational number.
</a></div></td><td><div style="text-align:center;">15463</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>41</b></div></td><td><div><a href="index.php?section=problems&amp;id=41" style="text-decoration:none;" title="Click to view problem">
What is the largest <i>n</i>-digit pandigital prime that exists?
</a></div></td><td><div style="text-align:center;">12250</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>42</b></div></td><td><div><a href="index.php?section=problems&amp;id=42" style="text-decoration:none;" title="Click to view problem">
How many triangle words does the list of common English words contain?
</a></div></td><td><div style="text-align:center;">14931</div></td></tr>

<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>43</b></div></td><td><div><a href="index.php?section=problems&amp;id=43" style="text-decoration:none;" title="Click to view problem">
Find the sum of all pandigital numbers with an unusual sub-string divisibility property.
</a></div></td><td><div style="text-align:center;">9909</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>44</b></div></td><td><div><a href="index.php?section=problems&amp;id=44" style="text-decoration:none;" title="Click to view problem">
Find the smallest pair of pentagonal numbers whose sum and difference is pentagonal.
</a></div></td><td><div style="text-align:center;">9500</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>45</b></div></td><td><div><a href="index.php?section=problems&amp;id=45" style="text-decoration:none;" title="Click to view problem">
After 40755, what is the next triangle number that is also pentagonal and hexagonal?
</a></div></td><td><div style="text-align:center;">14144</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>46</b></div></td><td><div><a href="index.php?section=problems&amp;id=46" style="text-decoration:none;" title="Click to view problem">
What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
</a></div></td><td><div style="text-align:center;">10035</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>47</b></div></td><td><div><a href="index.php?section=problems&amp;id=47" style="text-decoration:none;" title="Click to view problem">
Find the first four consecutive integers to have four distinct primes factors.
</a></div></td><td><div style="text-align:center;">10155</div></td></tr>

<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>48</b></div></td><td><div><a href="index.php?section=problems&amp;id=48" style="text-decoration:none;" title="Click to view problem">
Find the last ten digits of 1<sup>1</sup> + 2<sup>2</sup> + ... + 1000<sup>1000</sup>.
</a></div></td><td><div style="text-align:center;">25252</div></td></tr>
<tr class="bg_table_row1"><td style="height:40px;"><div style="text-align:center;"><b>49</b></div></td><td><div><a href="index.php?section=problems&amp;id=49" style="text-decoration:none;" title="Click to view problem">
Find arithmetic sequences, made of prime terms, whose four digits are permutations of each other.
</a></div></td><td><div style="text-align:center;">9724</div></td></tr>
<tr class="bg_table_row2"><td style="height:40px;"><div style="text-align:center;"><b>50</b></div></td><td><div><a href="index.php?section=problems&amp;id=50" style="text-decoration:none;" title="Click to view problem">
Which prime, below one-million, can be written as the sum of the most consecutive primes?
</a></div></td><td><div style="text-align:center;">10569</div></td></tr>

